Low-cost, high surface area inorganic membrane modules have been long sought by industry because of unique performance attributes of both metallic and ceramic materials. In order to be easily deployed, membrane modules need to include a compact form. Conventional reverse osmosis (RO) membranes packed with polymer membranes can provide a large membrane surface area per unit volume. However, reverse osmosis (RO) membranes are ineffective for mass transfer applications due to an inability to process sweep (i.e., gas) flow streams. RO-type membranes with their cylindrical designs are also limited by channel dimensions that can lead to large pressure drops when placed under vacuum. In addition, conventional filters that employ metal or ceramic tubes have a membrane packing density that is typically lower than polymer membranes by nearly one order of magnitude. In addition, spiral-wound RO membrane filters and plate-type RO membrane filters commonly used for desalination of sea water and for treatment of waste water in bio-reactors, respectively, provide filtration of only a single flow stream in a single flow direction. Neither filter can process dual flow streams simultaneously, which eliminates mass transfer and heat transfer between two flow streams. And, membrane filters designed for liquid-phase filtration are not suitable for vapor-phase separation at low pressures or under vacuum where pressure drops become a significant concern. Accordingly, new membrane designs are needed that provide high mass transfer rates with minimal pressure drops for liquid and vapor-phase separation and filtration applications. The present invention addresses these needs.